Valid cuts are viewed in the operations research literature as inequalities that strengthen linear relaxations. The constraint satisfaction community has developed an alternate approach. Logical inference methods, such as the resolution method, can generate valid cuts that need not be inequalities and that are considered apart from any role in relaxations. They reduce backtracking by helping to achieve “consistency,” which is analogous to integrality in a polyhedral setting. The basic theory underlying these methods is presented here. Parallels with mathematical programming are pointed out, and resolution- based algorithms for generating cuts are proposed as a unifying theme. Specific topics include k-consistency, adaptive consistency, the dependency graph, and various measures of its width, including induced width and bandwidth.


Search Tree Logic Programming Constraint Satisfaction Dependency Graph Constraint Satisfaction Problem 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • J. N. Hooker
    • 1
  1. 1.Graduate School of Industrial AdministrationCarnegie Mellon UniversityPittsburghUSA

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